Parallel and Nonparallel Distributed Compensation Controller Design for T-S Fuzzy Discrete Singular Systems With Distinct Difference Item Matrices

Liang Qiao,Linlin Li,Yanrong Lu

doi:10.1109/access.2021.3089496

Abstract

The issues of admissibility and controller design for a class of extended T-S fuzzy discrete singular systems (FDSSs) with distinct difference item matrices are discussed in this article. A new augmented system which is the equivalent of the original system is introduced to convert these distinct difference item matrices into the easy treatment form. On this basis, using the fuzzy Lyapunov function (FLF), relaxed sufficient condition is given to ensure the admissibility of unforced systems. This condition is described via strict linear matrix inequalities (LMIs), which facilitates to analyze the admissibility. Meanwhile, the design methods of parallel and nonparallel distributed compensation (PDC and Non-PDC) controllers are also proposed. Finally, the advantages of the developed admissibility and controller design approach are illustrated by three examples.

Highlights

Since T-S fuzzy systems [1] are used as a nonlinear function approximation tool, such systems are the wide variety of applications for the control problems of nonlinear systems
Using common Lyapunov function (CLF), stability and stabilisation problems of fuzzy systems are solved based on a series of linear matrix inequalities (LMIs) [9]
II) Using fuzzy Lyapunov function and matrix inequality method, a relaxed admissibility criteria for extended fuzzy discrete singular systems (FDSSs) is given in terms of strict LMIs

Summary

INTRODUCTION

Since T-S fuzzy systems [1] are used as a nonlinear function approximation tool, such systems are the wide variety of applications for the control problems of nonlinear systems. In [24], based on the CLF, the admissibility analysis and control issues for FDSSs with multiple difference matrices Ei at locally models are discussed, which increased the conservatism. Based on the new augmented system method, a relaxed sufficient condition is given for the admissibility of FDSSs via strict LMIs. considering the equivalence between the dual system and the original system, the PDC controller and Non-PDC controller design methods are given to ensure the admissibility for closed-loop FDSSs. it is showed that the proposed method is more effective and feasible by simulation examples. II) Using fuzzy Lyapunov function and matrix inequality method, a relaxed admissibility criteria for extended FDSSs is given in terms of strict LMIs. The slack matrices are introduced into this criteria to reduce the conservatism. Lemma 2.1 [26] Given matrices Φij ∈ Rn×n , the following two statements are equivalent

ADMISSIBILITY ANALYSIS

ILLUSTRATIVE EXAMPLES

CONCLUSION